Theorems · Theorem · commutative algebra

Valuation.Integers.isIntegral_iff_v_le_one

∀ {R : Type u} {Γ₀ : Type v} [inst : CommRing R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation R Γ₀}
  {O : Type w} [inst_2 : CommRing O] [inst_3 : Algebra O R], v.Integers O → ∀ {x : R}, IsIntegral O x ↔ v x ≤ 1

Defined in

Mathlib.RingTheory.Valuation.Integral

Cited by

1 results in Mathlib

Foundations

Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderedCommGroupWithZeroCommRingAlgebra